divide these fractions and simplify the answer.

Question

3x/16 divided by 3x-9/20

Answer 1

To divide the fractions \( \frac{3x}{16} \) by \( \frac{3x-9}{20} \), you can multiply by the reciprocal of the second fraction.

This means:

\[ \frac{3x}{16} \div \frac{3x - 9}{20} = \frac{3x}{16} \times \frac{20}{3x - 9} \]

Now, we can multiply the fractions:

\[ \frac{3x \cdot 20}{16 \cdot (3x - 9)} = \frac{60x}{16(3x - 9)} \]

Next, we simplify this expression.

1. Simplify \( 60x \) and \( 16 \): \[ \frac{60x}{16(3x - 9)} = \frac{15x}{4(3x - 9)} \]

2. Factor \( 3x - 9 \) in the denominator: \[ 3x - 9 = 3(x - 3) \]

   Substituting this back, we have: \[ \frac{15x}{4 \cdot 3(x - 3)} = \frac{15x}{12(x - 3)} \]

3. Now, simplify \( \frac{15x}{12(x - 3)} \): \[ \frac{15x}{12(x - 3)} = \frac{5x}{4(x - 3)} \]

Thus, the simplified answer is:

\[ \frac{5x}{4(x - 3)} \]

Answer 2

the real answer is 5x/4x-12

Answer 3

Let's go through the calculation step by step again to clarify the division of the fractions and ensure that we get the correct simplified form.

Problem Statement: You have: \[ \frac{3x}{16} \div \frac{3x - 9}{20} \]

Step 1: Convert the division into multiplication by the reciprocal. \[ \frac{3x}{16} \div \frac{3x - 9}{20} = \frac{3x}{16} \times \frac{20}{3x - 9} \]

Step 2: Multiply the fractions. \[ = \frac{3x \cdot 20}{16 \cdot (3x - 9)} = \frac{60x}{16(3x - 9)} \]

Step 3: Simplify the expression. First, let's simplify the numerator and the denominator:

1. Factor \(3x - 9\): \[ 3x - 9 = 3(x - 3) \]

2. Substitute this factor into the expression: \[ = \frac{60x}{16 \cdot 3(x - 3)} = \frac{60x}{48(x - 3)} \]

3. Now simplify \( \frac{60x}{48(x - 3)} \): \[ = \frac{5x}{4(x - 3)} \]

Final Result: Thus, the correct simplified expression is: \[ \frac{5x}{4(x - 3)} \]

Alternative Representation: Alternatively, if you want to represent it differently, you can express \(4(x - 3)\) as \(4x - 12\), leading to: \[ \frac{5x}{4(x - 3)} = \frac{5x}{4x - 12} \]

Therefore, both forms \(\frac{5x}{4(x - 3)}\) and \(\frac{5x}{4x - 12}\) are equivalent.

Thank you for your patience, and I hope this clears up any confusion!